Mesoscale & Continuum Modelling


The research of Modelling and Mechanics group aims to the investigation of new problems in mechanics of materials, optics, and quantum mechanics and its applications in nanosciences, mathematical biology and mathematical geophysics. The main focus of the group is in the continuum modelling of discrete atomistic problems, the constitutive modelling of graphene and germanium, the dynamics of optical waves in photonics graphene  and lattices, the dynamic behaviour of magnetic materials and skyrmionic textures, and in the semiclassical modelling of acoustic and elastic waves and quantum systems. The group develops novel models, new analytical methods and numerical techniques, and contributes to the training of graduate students and young researchers, with diverse background in physics, applied mathematics and engineering, working on these problems from different perspectives.


Continuum Modelling of Discrete Atomistic Problems:  Research on this field aims to the development of various techniques from discrete mathematics to provide exact connections of continuum and atomistic descriptions of crystalline solids, such as nanoparticles.  We have developed a new concept of lattice-cell average that allows such connections. We are able to provide explicit exact expressions for surface and edge energies of nanocrystals, for general interatomic potentials, and a new expression of the interfacial energy of deformation twins and phase boundaries, with extensions beyond pairwise interactions

Constitutive continuum modelling of Graphene and Germanium: Research in this area employs the arithmetic symmetry group to model materials used in emerging technologies, such as graphene, germanium, hexagonal boron nitride and others, in the discrete level. Confinement to weak transformation neighbourhoods and use of the Cauchy-Born rule allow for the transition from the discrete to the continuum description, where someone is able to work with the geometric symmetry group. The theory of invariants is used to build up generic expressions for the energy that fully capture material’s anisotropy at the continuum level both for the small and finite deformation regime. When there is no available representation theory one may use the theory of integrity basis to build the energy functions. Such energies describe in the most general way the mechanical response of materials at the microscale when they are scaled up to the continuum.

Semi-inverse methods: Closed form solutions that correspond to simple mechanical experiments are obtained from the system of momentum’s differential equations using semi-inverse methods. Simple tension/compression, indentation, wrinkling\buckling are examples of simple but important tests for the characterization of materials at the microscale. They serve as a guide for testing continuum theories of micro, nano materials against available experimental or computational results.

Optical beams and Structured light fields: Research in this area aims to the theoretical understanding and numerical simulation of optical waves in space and space-time, and their applications in different branches of optical engineering and photonics. The core of this activity concerns the generation of optical waves with engineered properties such as beam width, trajectory, and maximum amplitude, as well as the  propagation of invariant optical fields of the Airy and Bessel-type, and their applications in high-resolution microscopy and stealth technologies .

Periodic lattices: Research in this area deals with specific nonlinear aspects of light propagating in complex systems with periodic optical indices.  Especially we focus on the dynamics in different types of lattices and the understanding of topological phenomena, gauge fields, dynamic localization and coherent destruction of tunneling, and also the interplay between pseudospin, isospin, and vorticity in photonic graphene.

Nonlinear dynamics in magnetic materials: Research in this area aims to the investigation of the rich micromagnetic structure and the description of a variety of patterns at the mesoscale and the nanoscale. Physico-mathematical studies in this field focus on magnetic solitons, which are topological in nature, and they are motivated by and combined with the strong technological interest from the high-tech  industry on magnetic materials, including magnetic storage, magnetoresistive-RAM applications, spin-torque oscillators, and magnetic diodes. The models include domain walls in one spatial dimension, vortices and skyrmions in two dimensions, and vortex rings in three dimensions, and they are modeled by various forms and generalisations of the Landau-Lifshitz equation, which lead to different interesting and useful dynamics of  topological magnetic solitons.

Solitons in condensed matter physics: Topological solitons arise in a great variety of condensed matter systems, as well as in cosmology and in nonlinear optics. The research in this direction focus on the investigation of ultra-cold gases that form Bose-Einstein condensates (BECs), which are of particular interest to quantum technology. Quantised vortices (or superfluid vortices) are found as solutions of Gross-Pitaevskii models. The tunability of gaseous BECs allows for complicated structures, such as vortex rings that propagate in a cylindrical BEC, to be formed. The study of these systems is based on the theory of conservation laws and the numerical simulation of the nonlinear model.

Semiclassical modeling of wave and quantum systems: Research in this direction focuses on the semiclassical asymptotics of wave and  Schrodinger equations, via phase space techniques, which are very powerful for the construction of uniform (caustic-free) solutions of the Cauchy problem with highly oscillatory data, and the investigation of propagating singularities and beam-type solutions, in acoustics, seismology, optics and quantum mechanics. Techniques from microlocal analysis (Fourier integral operators) and deformation quantization (Wigner and wave-packet transforms) are employed  to device phase space equations governing energy density and flux propagation. Asymptotic solutions are constructed using stationary phase approximations for complex phases, that are able to describe essential wave and quantum effects in phase space far away from classical Lagrangian manifolds. 

Education and Training:  The group contributes to the education and training of undergraduate, graduate and post-graduate students as well as of PhD candidates and Postdoctoral researchers.

Mesoscale & Continuum Modelling



S. Komineas and N. Papanicolaou (2020) Traveling skyrmions in chiral antiferromagnets, SciPost Phys. 8, 086 

S. Komineas, C. Melcher, S. Venakides (2020) Chiral skyrmions of large radius, arXiv:1910.04818 

S. Komineas, C. Melcher, S. Venakides (2020) The profile of chiral skyrmions of small radius Nonlinearity 33, 3395-3408 

S. Komineas, C. Melcher, S. Venakides (2019) Traveling domain walls in chiral ferromagnets Nonlinearity 32, 2392-2412 

N. Sisodia, S. Komineas, P. K. Muduli (2019) Chiral skyrmion auto-oscillations in a ferromagnet under spin transfer torque Phys. Rev. B 99, 184441

G. Grekas, M. Proestaki, P. Rosakis, J. Notbohm, C. Makridakis,   G. Ravichandran, Cells exploit a phase transition to establish interconnections in fibrous extracellular matrices, (2019) arXiv:1905.11246
R. Tomasello, S. Komineas, G. Siracusano, M. Carpentieri, G. Finocchio, Chiral skyrmions in an anisotropy gradient driven by spin-Hall effect, Phys. Rev. B 98, 024421 (2018)

Efremidis, N. K. (2017). Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type, Opt. Lett. 42, 5038 (2017).

Goutsoulas, M.; Paltoglou, V. and Efremidis, N. K. (2017) Cross-phase modulation mediated pulse control with Airy pulses in optical fibers, J. Opt. 19, 115505

Efremidis, N. K.; Nye, N. S.; and Christodoulides, D. N. (2017) Exact bidirectional X-wave solutions in fiber Bragg gratings, Phys. Rev. A 96, 043820

Roussou, A.; Smyrnakis, J.; Magiropoulos, M.; Efremidis, N. K. and Kavoulakis, G. M. (2017) Rotating Bose-Einstein condensates with a finite number of atoms confined in a ring potential: Spontaneous symmetry breaking, beyond the mean-field approximation, Phys. Rev. A 95, 033606

Paltoglou V. and Efremidis, N. K. (2017) breaking in a nonlinear double-slit configuration, J. Opt. Soc. Am. B 34, 257 (2017).

Efremidis, N. K. and Mparkas, (2017) M. Nonlinear imaging in photonic lattices, Opt. Lett. 42, 147.

Komineas, S., Shipman, S.P., Venakides, S. (2016). Lossless polariton solitons, Physica D 316, 43-56.

P. Rosakis, The Interfacial Energy of a Phase Boundary via a Lattice-Cell Average Approach (2016), arXiv:1603.02985

Penciu, R.-S., Makris, K. G and Efremidis, N. K. (2016) Nonparaxial abruptly autofocusing beams, Opt. Lett. 41, 1042

Notbohm, J., Lesman, A., Rosakis, P., Tirrell, D.A., Ravichandran, G., (2015). Microbuckling of fibrin enables long range cell mechanosensing, Journal of the Royal Society Interface 12 (108) 20150320. arXiv:1407.3510

Komineas, S. and Papanicolaou, N., (2015). Skyrmion dynamics in chiral ferromagnets under spin-transfer torque, Phys. Rev. B 92, 174405

Rosakis, P., Notbohm, J., Ravichandran, G., (2015). A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells, Journal of the Mechanics and Physics of Solids 85 16-32. arXiv:1412.2612.

Roussou, A. ; Tsibidis, G. D. ; Smyrnakis, J. ; Magiropoulos, M. ; Efremidis, N. K. ; Jackson, A. D. and Kavoulakis G. M. (2015) Hysteresis and metastability of Bose-Einstein condensed clouds of atoms confined in ring potentials, Phys. Rev. A 91, 023613 (2015)

Song, D. ; Paltoglou, V. ; Liu, S. ; Zhu, Yi; Gallardo, D.; Tang, L.; Xu, J.; Ablowitz, M.;. Efremidis, N. K and Chen Z. (2015) Unveiling pseudospin and angular momentum in photonic graphene, Nat. Commun. 6, 6272

Paltoglou, V.; Chen, Z. and Efremidis, N. K. (2015) Composite multi-vortex diffraction-free beams and van Hove singularities in honeycomb lattices, Opt. Lett. 40, 1037

Wu, Z.; Zaremba, E.; Smyrnakis, J.; Magiropoulos, M.; Efremidis, N. K and Kavoulakis G.M., (2015) Mean-field yrast spectrum and persistent currents in a two-component Bose gas with interaction asymmetry, Phys. Rev. A 92, 033630.

Zhao, J.; Chremmos, I. D.; Song, D.; Zhang, P.; Christodoulides, D. N.;  Efremidis, N. K. and Chen, Z. (2015) Curved singular beams for three-dimensional particle manipulation, Sci. Rep. 5, 12086

Song, D.; Liu, S.; Paltoglou, V.; Gallardo, D.; Tang, L.; Zhao, J.; Xu, J.; Efremidis, N. K. and Chen Z. (2015) Controlled generation ofpseudospin-mediated vortices in photonic graphene, 2D Mater. 40, 034007.

Zhao, J.; Chremmos, I. D.; Zhang, Ze; Hu, Yi; Song, D.; Zhang, P.; Efremidis, N. K. and Chen, Z. (2015) Specially shaped Bessel-like self-accelerating beams along predesigned trajectories, Sci. Bull. 60, 1157 (2015).

Penciu, R.-S.; Paltoglou, V. and Efremidis N. K., (2015) Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories, Opt. Lett. 40, 1444

Paltoglou V. and Efremidis, N. K. (2015) Modifying the optical path in a nonlinear double-slit experiment, Opt. Lett. 40, 5208.

Chen, Z.; Zhao, J.; Chremmos, I. D.; Song, D.; Christodoulides, D. N. and Efremidis, N. K. (2015) Spiraling particles by fineshaped dynamical singular beams, Opt. Photonics News 26, 44 (December 2015).

P. Rosakis, Continuum surface energy from a lattice model,  Networks and Heterogeneous Media  9(3), 453-476 (2014)

Komineas, S. and Papanicolaou, N., (2015). Skyrmion dynamics in chiral ferromagnets, Phys. Rev. B 92, 064412

Zhang, S., Baker, A.A., Komineas, S., and Hesjedal, Th. (2015). Topological computation based on direct magnetic logic communication, Scientific Reports 5, 15773

Komineas, S., Shipman, S.P., Venakides, S. (2015). Continuous and discontinuous dark solitons in polariton condensates, Phys. Rev. B 91, 134503.

Komineas, S., (2015). Magnetization oscillations by vortex-antivortex dipoles, Physica D 291, 8-16.

Efremidis N. K., (2014) Accelerating beam propagation in refractive index potentials, Phys. Rev. A 89, 023841

Makris, K. G.; Kaminer, I. ; El-Ganainy, R. ; Efremidis, N. K. ; Chen, Z.; Segev, M. and Christodoulides, D. N. (2014) Accelerating diffraction-free beams in photonic lattices, Opt. Lett. 39, 2129

Bolpasi, V.; Efremidis, N. K.; Morrissey, M. J.; Condylis, P.; Sahagun, D.; Baker M. and von Klitzing W. (2014) An ultra-brightatom laser, New J. Phys. 16, 033036.

Smyrnakis, J.; Magiropoulos, M.; Efremidis, N. K and. Kavoulakis, G. M (2014) Persistent currents in a two-component Bose-Einstein condensate confined in a ring potential, J. Opt. B Quantum Semiclassical Opt. 47, 215302

Zhao, J.; Zhang, P.; Deng, D.; Liu, J.; Gao, Y.; Chremmos, I. D.; Efremidis, N. K.; Christodoulides, D. N. and  Chen, Z. (2013) Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories, Opt. Lett. 38, 498

Efremidis, N. K.; Paltoglou, V.; and von Klitzing, W. (2013) Accelerating and abruptly autofocusing matter waves, Phys. Rev. A 87, 043637

Chremmos, I. D.; Fikioris, G. and Efremidis, N. K.  (2013) Accelerating and abruptly-focusing beam waves in the Fresnel zone of antenna arrays, IEEE Trans. Antennas Propag. 61, 5048

Chremmos, I. D. and Efremidis, N. K., (2013) Nonparaxial accelerating Bessel-like beams, Phys. Rev. A 88, 063816 (2013).

Finocchio, G., Puliafito, V., Komineas, S., Torres, L., Ozatay, O., Hauet, T., Azzerboni, B., (2013). Nanoscale spintronic oscillators based on the excitation of confined soliton modes, J. Appl. Phys. 114, 163908


  • Nikos Efremidis
  • Spyros Kamvisis
  • Stavros Komineas
  • George Makrakis
  • Phoebus Rosakis
  • Dimitris Sfyris
  • Riccardo Tomasello


For any information regarding the Group, please contact:
Mesoscale Modelling Group
Institute of Applied and Computational Mathematics
Foundation for Research and Technology - Hellas
Nikolaou Plastira 100, Vassilika Vouton,
GR 700 13 Heraklion, Crete

Tel: +30 2810 391800
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. (Mrs. Maria Papadaki)

Tel.: +30 2810 391805
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. (Mrs. Yiota Rigopoulou)